The formation of shear shock waves in the brain has been proposed as one of the plausible explanations for deep intracranial injuries. In fact, such singular solutions emerge naturally in soft viscoelastic tissues under dynamic loading conditions. To improve our understanding of the mechanical processes at hand, the development of dedicated computational models is needed. The present study concerns three-dimensional numerical models of incompressible viscoelastic solids whose motion is analysed by means of shock-capturing finite volume methods. More specifically, we focus on the use of the artificial compressibility method, a technique that has been frequently employed in computational fluid dynamics. The material behaviour is deduced from the Fung--Simo quasi-linear viscoelasiticity theory (QLV) where the elastic response is of Yeoh type. We analyse the accuracy of the method and demonstrate its applicability for the study of nonlinear wave propagation in soft solids. The numerical results cover accuracy tests, shock formation and wave focusing.

翻译：脑内剪切冲击波的形成已被提出为深层颅内损伤的合理解释之一。事实上，此类奇异解在动态载荷条件下会自然出现在软粘弹性组织中。为了增进对当前力学过程的理解，需要开发专用的计算模型。本研究涉及不可压缩粘弹性固体的三维数值模型，其运动通过激波捕捉有限体积法进行分析。具体而言，我们聚焦于人工可压缩性方法的应用，这是一种在计算流体动力学中常用的技术。材料行为基于 Fung--Simo 拟线性粘弹性理论推导，其中弹性响应为 Yeoh 类型。我们分析了该方法的精度，并论证了其在研究软固体中非线性波传播问题的适用性。数值结果涵盖了精度测试、冲击波形成与波聚焦分析。